The government's scientific advisory group has said it "does not have confidence" the R number is currently below the crucial figure of 1 in England.
The latest estimate puts the R rate - which refers to the number of people on average that an infected person passes the virus on to - at between 0.8-0.9.
In the North West, where new restrictions have been imposed in some areas, the R has risen from 0.7-1 last week to 0.8-1.1 this week.
But SAGE said the estimates represent the transmission of coronavirus from several weeks ago, as there is a delay between people becoming infected and needing healthcare.
"Estimates that use more timely data reflecting infections suggest a higher R for England than shown here. As a result, SAGE does not have confidence that R is currently below 1 in England," it said on the government website.
There has also been a slight increase in the number of people testing positive for coronavirus in England, new data shows.
According to the Office for National Statistics (ONS), between 20 and 26 July there were around 4,200 new infections in the community per day.
This is up from an estimated 2,800 new cases a day the previous week.
But the numbers are not enough evidence to say yet "with confidence" whether infection rates differ by region, the ONS has said.
Some lockdown restrictions have been reimposed in virus hotspots in the north of England following a spike in infections.
People in Greater Manchester, East Lancashire and parts of West Yorkshire are now banned from meeting other households indoors, in a move described by Health Secretary Matt Hancock as "absolutely necessary".
A total of 846 new cases were reported, the most since 901 cases were announced on 28 June.
There is some discrepancy between Department of Health and ONS figures on coronavirus infections, as the government figures do not include people who are infected but do not test positive.
This is either because they are not showing symptoms or because they do not get tested.
The ONS attempts to estimate the true level of infection, meaning its figures have at times been more than four times higher than the government figures suggest.
Here's what each column in the above chart shows:
Cases: The total number of confirmed COVID-19 cases since the beginning of the outbreak
Rate: The number of cases per 100,000 people
Two weeks: The number of confirmed cases over the past fortnight
Two-weeks rate: The number of cases per 100,000 people over the past fortnight
The government has expressed concerns about a potential second wave of infections, with Boris Johnson warning Britons to be wary of a "really damaging second wave".
The health secretary also said he was "worried" after seeing a "second wave starting to roll across Europe".
Analysis: 'Any rise in the number of infections will be taken very seriously'
By Ashish Joshi, health correspondent
The latest ONS figures confirm what many had predicted: that the easing of lockdown measures would lead to a rise in the number of infections.
The virus has only been suppressed but not eliminated from our communities.
So as soon as people are allowed to move and mix, even with social distancing measures in place, there is bound to be an uptick in the number of infections.
The same has been happening in some parts of Europe and we have seen restrictions reimposed in Greater Manchester, and parts of West Yorkshire and East Lancashire.
But these latest ONS figures do not highlight any regional variations. That is because it uses a smaller sample set.
The government will use these ONS figures and its own local intelligence, working closely with Public Health England, to make decisions.
We must allow a degree of uncertainty with these figures.
The sample survey has been extrapolated to give us a picture of what might be happening in the community with the virus.
We can see the data shows the number of people getting infected remained flat and the curve on the graph had been steadily downwards, before levelling off. It now shows an increase.
This does not mean we will see a spike but any rise in the number of infections will be taken very seriously.